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The Influence of Money in MLB, 1985-2014

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The Star-Ledger-USA TODAY Sports

In 2014, for the 21st straight year, the Yankees finished ahead of the Jays in the AL East standings. In 2014, for the 21st straight year, the Yankees had a higher payroll than the Jays. 1993 was the last time the Jays outspent the Yankees, and it was the last time they finished ahead of them too. Perhaps unsurprisingly given these facts, 1993 was also the last time the Jays made the playoffs.

Related to this, last week there was some discussion about what this fact pattern meant in terms to the influence of payroll on winning, which MLB has tried to address for most of Bud Selig's tenure. BBB commenter lb.wood pointed to some research suggesting MLB had not been able to influence. I was not particularly impressed by the research, so decided to look into it further - basically, how has the relationship between payroll and winning changed over the last couple decades?

I started with the Lehman database, which has salary data going back to 1985. As the 2014 update is not yet out, and I the most recent version I had downloaded was 2012, for 2013-14 I used USA Today salary info, and in total that gave 30 seasons.

For each team season, I calculated the team's Wins Above Replacement (WAR), based on the unified Fangraphs/Baseball-Reference replacement level of 1,000 WAR / MLB season of 2,430 games. As a reminder, over a season of 162 games, a replacement level team would be expected to win about 48 games, and an average team going 81-81 will total 33 WAR. For the strike-shortened 1994-95 seasons, I prorated each team's season to 162 games to make them directly comparable with other seasons.

Likewise, on the payroll side I calculated both total team payroll and Payroll Above Replacement (PAR) based on the Lahman data (with minor adjustments for a few teams in 1987 where the data was clearly incomplete). A replacement level payroll was based on the minimum salary for a given season for an entire 40-man roster. In reality, not all players on the 40-man will be in MLB and making the minimum, but given injuries and the implausibility of having all minimum salaried players on the 25-man, this represents a reasonable proxy of the bare minimum a team would have to spend. In 1985, the minimum salary was $60,000 resulting in a replacement level payroll of $3-million per team; by 2014 it was up to $20-million based on a minimum of $500,000.

In order to control for salary inflation and enable valid comparison across time, for each year I calculated the standard deviation of team payroll, and used it to standardize each team's payroll relative to league league (Standardized PAR or SPAR). To give an example, the average team PAR in 2014 was $99.7-million, with a standard deviation of $44-million. The Jays' team PAR was $117-million, which is 0.4 standard deviations above average, and hence that's their 2014 SPAR.

By regressing each team's WAR in a season against their SPAR, we can see the average effect of money over the last 30 years (858 team seasons):

The positive relation between the team payroll and winning is clear: the more a team's payroll relative to league average, the more they win. Over the last 30 years, on average one standard deviation of payroll results in a change of just over 4 wins, and this is highly a significant factor (standard error = 0.36, t=11.4, F=130.3 for the regression). In the 2014 context, this implies that it would cost about $10-million to buy a win. However, it should be noted that that differences in payroll only explains about 13% of the difference in winning. That's actually quite good for a one factor model, but it also means that there's a lot of variation in winning that's not explained by variation payroll. Certainly, payroll is not destiny.

But what we really want to know is how this has changed over time. One approach would be to look at the relationship of wins and payroll for each year, but on a seasonal level with a sample of just 26-30, there's too much noise to draw meaningful results (for the 1987 season, the relationship is negative, which is nonsensical). Instead, I've divided the 30 years into groups. Initially I did six periods of 5 years each, starting with 1985-89 and finishing with 2010-14. However, given similarities between periods, for simplicity it makes more sense to discuss in 10 year intervals. However, I will also show summary data for each 5 year sub-period. At the end, I have an appendix that reports the same results as below for each individual season for those interested.

1985-94

Time Period Average PAR S.D. of PAR Relationship R^2 S.E. of SPAR 95% Win Interval for SPAR for P(X)>80%
+2 SPAR +3 SPAR 90W 95W 100W
1985-94 $17.2 $5.3 WAR = 33.3 + 2.3*SPAR 0.046 0.65 83 - 88 84 - 92 5.1 8.0 10.8
1985-89 $10.1 $3.1 WAR = 33.2 + 2.2*SPAR 0.041 0.95 82 - 89 82 - 93 6.4 10.0 13.6
1990-94 $24.3 $7.5 WAR = 33.3 + 2.4*SPAR 0.051 0.89 82 - 89 83 - 93 5.5 8.5 11.5

For the initial time period of 1985-94, the link between payroll and winning is quite weak, much weaker than the overall link for the past 30 years. The relationship is not quit random, but team payroll is explaining less than 5% of differences in winning (R^2).

Let's breakdown the numbers. Next to the time period is the payroll above replacement for the average team from 1984-95. Because payrolls increased substantially during this time (more than doubling from 1985-89 to 1990-94), it makes more sense to look at the 5 years intervals for these. Next is the average seasonal standard deviation of PAR. At $5.3-million for the period relative to a $17.2-million, it means that to double league average a team would have have been 3 to 4 standard deviations above average, which is way off the curve.

Next is the actual relationship between WAR and SPAR. The important part is the multiple for SPAR, which is 2.3 for 1985-1989. For each extra standard deviation of payroll (again, $5.3-million), a team could expect to add about 2.3 wins. Next to that is the R^2 of the regression and the standard error on the SPAR variable (for those who like to see the statistical nitty gritty).

Finally, the two major columns and subcolumns on the right attempt to quantify how significant the regression results are. First, are expected win intervals for teams who spent at 2 and 3 standard deviations above average. For 1985-94, this would mean spending roughly $10-million or $15-million respectively more than average, or roughly 65% and 100% above average. A team at 2 SPAR ($10M) above average would expect to win 83-89 games 95% of the time, and a team at 3 SPAR would expect to win 84-92 games 95% of the time. So you'd expect to be a very good team, but this falls way short of guaranteeing a playoff spot, especially since this was pre-wild card when the target was usually around 95 wins.

The final piece of information is the spending that would be required to give a team an 80% chance of winning at least 90, 95 and 100 games respectively. 90 wins is more relevant for the wild card era, as teams winning at least 90 games made the playoffs over 80% of the time. 95 is roughly the average to win one's division both pre- and post-wild card, and 100 wins essentially made a team a lock to win the division in both eras. From 1985-89, to have an 80% chance of winning 95-100 games based on payroll alone would have required spending at 8 to 10 deviations above average, or spending roughly $60 to $70-million on payroll when the league average was $20-million. Simply, this was not really feasible.

1995-2004

Time Period Average PAR S.D. of PAR Relationship R^2 S.E. of SPAR 95% Win Interval for SPAR for P(X)>80%
+2 SPAR +3 SPAR 90W 95W 100W
1995-04 $47.1 $20.1 WAR = 33.3 + 5.7*SPAR 0.216 0.64 90 - 95 94 - 102 1.7 2.7 3.7
1995-99 $35.8 $13.9 WAR = 33.3 + 6*SPAR 0.273 0.83 90 - 96 94 - 104 1.7 2.6 3.6
2000-04 $58.4 $26.3 WAR = 33.3 + 5.4*SPAR 0.174 0.97 88 - 96 91 - 103 2.0 3.1 4.1

Just from the graphic alone, it should be obvious that over the next ten years, money and winning were much more tightly linked, and the data backed this up. The average team PAR continued to increase, more than doubling over the 10 year period, though decelerating from the 1990-94 period. Of course, it's not just the average that matters, so does the distribution, and that increased as well (measured by the standard deviation).

The most significant thing is that spending mattered a lot more for winning in this period. Whereas previously each SPAR resulted in 2.3 more expected wins, from 1995-2004 the expectation was 5.7 runs (and pretty consistent breaking down into 5 year periods). In other words, there was a much higher payoff to spending more money.

The implications of this are obvious, looking at the win intervals for 2 and 3 SPAR (roughly $40- or $60-million above the PAR of $47-million), which are 90-95 wins and 94-102 wins. In other words, enough wins to virtually guarantee a playoff spot, and likely a division title. Likewise, spending enough to have an 80% chance of winning 90, 95 or 100 games only took about 2-4 standard deviations above average, which is a lot, but much more feasible than 8 or 10 as was the case for the previous ten years. This was the time period when the Yankees, Braves and Red Sox dominated, and to a certain degree, money was destiny, or at least seemed to be.

2005-14

Time Period Average PAR S.D. of PAR Relationship R^2 S.E. of SPAR 95% Win Interval for SPAR for P(X)>80%
+2 SPAR +3 SPAR 90W 95W 100W
2005-14 $80.0 $37.8 WAR = 33.3 + 4.2*SPAR 0.146 0.58 87 - 92 90 - 97 2.4 3.8 5.1
2005-09 $78.8 $34.4 WAR = 33.3 + 4.9*SPAR 0.214 0.77 88 - 94 91 - 100 2.1 3.3 4.5
2010-14 $87.8 $41.1 WAR = 33.3 + 3.5*SPAR 0.094 0.88 84 - 91 86 - 97 3.3 5.1 6.9

In the last 10 years, things have got better, and particularly in the last 5 years. Payroll is still a much larger influence then it was from 1985-94, but not as much as 1995-2004. Rather than a standard deviation of payroll resulting in 5.7 extra expected wins, it was only 4.2. But, even this is misleading, as it was 4.9 from 2005-09, falling down to only 3.5 in the last 5 years, which is not that different than the late 80s and early 90s.

Likewise, it's not so easy to buy a playoff spot either. A team spending with a SPAR of 2 (for 2014, this would mean roughly $210-million total payroll vs. league average of $120-million) would expect to win somewhere in the high-80s to low-90s, which is not enough to lock up a playoff spot. To really lock up a playoff spot for sure, total expenditure would have to be north of $250-million. Otherwise, as the Yankees have found out the last couple years, you can spend a lot and still end up golfing in October.

It seems that to a certain extent, MLB's efforts at limiting spending by the upper market teams is working. After reaching an apex in 1995-99, the link between payroll and winning has declined, to the point where it's not really feasible to spend enough to essentially guarantee a playoff spot.

One Additional Approach

To try and confirm the above trends, I looked at one final measure. For all 30 years, I took payroll ratio between the team with the 6th highest payroll and 6th lowest payroll. This measures the difference between spending by quite-well-off teams and quite-poor-off teams (essentially the 20th and 80th percentile, or about one standard deviation above and below average). The bigger it is, the greater the disparity.

Essentially, we see the same trend. From 1985 to the end of the 1990s, MLB spending on payrolls was getting more and more unequal. Since then, it has significantly moderated, though remaining above where it was 30 years ago.

APPENDIX

Year PAR S.D. PAR Inter Slope SE T-stat
1985 $8.8 $2.4 33.2 4.14 2.42 1.72
1986 $10.1 $3.1 33.2 2.30 2.04 0.26
1987 $9.5 $3.1 33.3 -0.92 2.00 -2.92
1988 $10.0 $3.3 33.2 2.09 2.41 -0.32
1989 $12.1 $3.5 33.2 3.53 1.90 1.63
1990 $13.7 $3.8 33.3 0.05 1.85 -1.80
1991 $20.9 $6.8 33.3 2.34 1.92 0.42
1992 $28.0 $9.2 33.3 0.28 2.08 -1.81
1993 $28.9 $9.3 34.1 4.28 2.23 2.05
1994 $30.0 $8.6 33.6 4.60 1.97 2.63
1995 $30.5 $9.5 33.1 3.72 2.13 1.59
1996 $30.9 $10.7 33.3 5.57 1.62 3.95
1997 $35.3 $13.1 33.0 4.43 1.67 2.76
1998 $37.6 $15.5 35.4 9.02 1.90 7.12
1999 $44.8 $20.6 33.9 7.13 1.93 5.20
2000 $50.0 $21.4 33.6 3.37 1.78 1.59
2001 $59.6 $24.6 34.0 4.25 2.33 1.92
2002 $59.0 $24.7 33.7 6.60 2.49 4.10
2003 $62.7 $28.0 33.3 5.65 2.29 3.36
2004 $60.7 $32.7 34.7 7.33 2.15 5.18
2005 $64.2 $34.3 34.0 5.37 1.78 3.59
2006 $68.5 $32.3 33.6 5.46 1.60 3.86
2007 $71.9 $33.9 32.7 4.57 1.53 3.04
2008 $78.4 $37.8 31.9 3.59 1.98 1.61
2009 $78.0 $33.9 32.2 5.40 1.90 3.50
2010 $79.6 $38.3 33.0 4.06 1.93 2.13
2011 $81.2 $40.8 32.4 4.63 1.97 2.65
2012 $84.2 $36.5 34.0 2.24 2.22 0.02
2013 $94.0 $45.8 33.5 3.84 2.20 1.64
2014 $99.7 $44.2 34.7 2.57 1.75 0.82